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anonymous

  • 4 years ago

limit of (5x+2)/sqrt(9x^2+3x+1)-x as x approaches -infinity

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  1. anonymous
    • 4 years ago
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    \[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+3 x+1}-x},x\to \text{Infinity}\right]=\frac{5}{2} \]

  2. anonymous
    • 4 years ago
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    rob its approaching negative infinity

  3. anonymous
    • 4 years ago
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    also can you please demonstrate in steps. i need to understand how to to dow this. and the denominator is actually sqrt(9x^2+x-3) sorry

  4. anonymous
    • 4 years ago
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    crap let me rewrite the question... i made alot of mistakes

  5. anonymous
    • 4 years ago
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    \[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]

  6. anonymous
    • 4 years ago
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    Sorry. missed the -infinity requirement.\[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+ x-3}},x\to -\text{Infinity}\right]=-\frac{5}{3}=1.6667 \]A plot of the problem expression from -100 throught zero is attached. Cannot help you on the solution process. Using Mathematica for the answers and plot generation.

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  7. anonymous
    • 4 years ago
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    ok this is the last one, do you think you can help me \[\lim_{x \rightarrow infinity}\sqrt{x^2+3x+1}-x\]

  8. anonymous
    • 4 years ago
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    I'll try

  9. anonymous
    • 4 years ago
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    \[\text{Limit}\left[\sqrt{x^2+3 x+1}-x,x\to \text{Infinity}\right]=\frac{3}{2}=1.5 \]Refer to the attached plot.

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